The purpose of this study was to develop vocabulary materials to aid non-native English speakers, specifically Russian speaking test-takers, in their preparation for the mathematical sections of the General Record Examination (GRE) and the Graduate Management Admission Test (GMAT) in terms of English mathematical vocabulary. GRE and GMAT preparation materials and practice tests published by the Educational Testing Service, Kaplan, and Barron's were analyzed with the help of computer software. This data was then used to determine which key words to include in the vocabulary tool, which is now available on Quizlet (www.quizlet.com). The developed materials were further proofread by competent mathematics and English language professionals and assessed with the help of a questionnaire administered to them. The rationale of the materials development and the procedures used for the process are described in detail in this thesis project.

The purpose of this study was to investigate how writing in mathematics is treated in one 4th grade National Science Foundation (NSF)-funded mathematics textbook titled Everyday Mathematics and one publisher-generated textbook titled enVision MATH. The developed framework provided categories to support each of the research questions. The results indicate that writing is supported in both traditional and NSF developed 4th grade mathematics textbooks Results also indicated the number of exercises and writing prompts was higher in the enVision MATH textbook. However, Everyday Mathematics had a higher percentage of exercises that were coded as writing prompts. The framework domains of content strand in enVision MATH and Everyday Mathematics are similar in percentages with the exception of prompts coded in the other category. Everyday Mathematics appeared to be the only textbook analyzed to support writing across different content areas. Furthermore, the content strand of number sense had the largest percentage of writing prompts coded between both textbook series. Other findings from this study suggest that the type of vocabulary coded within the writing prompts was similar in all categories between both textbook series analyzed. Additionally, vocabulary specific to the domain of mathematics and symbols appeared to have the largest percentage in this category for both textbook series. The teacher and student editions were explored in enVision MATH and Everyday Mathematics to provide more depth to the research. An exploration of the teacher edition indicated how writing was supported for instructional purposes. The teacher editions in both textbook series had the largest percentage of support in the form of one sample response. Within the student edition category, the layout varied in the enVision MATH and Everyday Mathematics textbook series. As a result, only the language of Everyday MATH could be analyzed for patterns in the sections, sub-sections, and additional sub-sections of where the prompts were located. Although this investigation did not involve analyzing student responses to the writing prompts, the findings provide information regarding the expectations of the writer in order to construct a mathematical response. For example, the domain specific vocabulary (DSV) and symbols category was rated the highest in percentage for both textbooks indicating that students will need to have command of the language and symbols of mathematics in order to engage in meaning making written discourse. Because most of the math prompts were specific to the problem solving category, it was determined after a linguistic analysis that the affordance of the prompt is much more complex than then binary categories of content and process Additionally, in order for students to respond to these content writing prompts, many process words known as meta-language (i.e., explanation, description, why question, how question) need to be comprehended in order for composition to begin. In light of these findings, I recommend that special attention be given to the teacher and student editions regarding the implementation of writing in mathematics. The development of these materials has important implications regarding instruction and learning of mathematical concepts through writing, potentially impacting student performance on national and international assessments.

Thesis (M.Ed. (Mathematics Education)) -- University of Limpopo, 2022 / A classroom in which learners are afforded opportunities to engage in meaningful mathematical discourse (Sfard, 2008) is desirable for the effective teaching and learning of mathematics. However, engagement in mathematical discourse requires learners to use appropriate mathematical vocabulary to think, learn, communicate and master mathematics (Monroe & Orme, 2002). Hence, I have undertaken this study to explore how mathematical vocabulary is used during mathematical classroom discourse using the lens of the commognitive framework. I chose a qualitative approach as an umbrella for the methodology with ethnography as the research design whereby participant observation, structured interviews and documents were used to collect data. One Grade 9 mathematics classroom with 25 learners and their mathematics teacher were purposefully selected as participants in the study. During data analysis, I looked at Sfard’s (2008) constructs of the commognitive theory to analyse the data and identify the mathematics vocabulary used in the discourse. This was followed by the use of realisation trees that I constructed for the teacher and learners’ discourse, which I used to identify learners thinking as either being explorative or ritualistic. Results indicate that both the teacher and learners use mathematical vocabulary objectively with positive whole numbers to produce endorsed narrative regulated by explorative routines. However, with algebraic terms both positive and negative, the teacher and learners’ discourse is mostly disobjectified, and produces narratives that are not endorsed and are regulated by ritualistic routines. It also became evident that the mathematical vocabulary that the teacher and learners use in the classroom discourse includes words that are mathematical in nature and colloquial words that learners use for mathematical meaning. v Furthermore, learners’ responses to the given mathematics questions which they are solving are mostly correct, hence it can be argued that the learners’ narratives were endorsed. However, their realisation trees indicates that learners were not working with mathematical objects in their own right (Sfard, 2008) and hence their narratives were not endorsed. I have recommended in this study, that teachers need to be cautious when operating with entities and not separate operations from their mathematical terms. Furthermore, the department of basic education, during workshops should encourage educators to always request reasons from learners substantiating their answers to questions in order to enhance their explorative thinking.

Some learners in South Africa perform poorly in school, especially in Mathematics. In 2010 the Department of Basic Education announced their concern regarding the pass rate. The National Education Department circulated a report in 2008 on some Grade 3 and Grade 6 learners who took part in a research project and only achieved level one and two in literacy (vocabulary), as well as numeracy (Mathematics). Several factors contribute to this shocking situation, such as the absence of the use of meta-cognitive strategies, number strategies, as well as language strategies. The prime goal of this study was to investigate the use of meta-cognitive strategies and Mathematical vocabulary during problem solving by Grade 7 learners. Three primary schools were invited to participate in the qualitative investigation. From these schools three top achievers (one per school) and three under-achievers (one per school) were invited to participate in the quantitative investigation. The study includes the results of the quantitative aspects of the investigation. Learners had to answer questions about predictions, achievements, control, as well as evaluation during the quantitative investigation. During this process, most of the learners predicted that they would do well and evaluated that they did well, but their marks for the questions about their achievements and control were in fact different. It is important to inform Mathematics teachers and learners about meta-cognitive strategies and Mathematical vocabulary, and the influence it can have on the learners’ achievements, as well as the positive effect during the learning of Mathematics. / MEd (Mathematics Education), North-West University, Potchefstroom Campus, 2014

Some learners in South Africa perform poorly in school, especially in Mathematics. In 2010 the Department of Basic Education announced their concern regarding the pass rate. The National Education Department circulated a report in 2008 on some Grade 3 and Grade 6 learners who took part in a research project and only achieved level one and two in literacy (vocabulary), as well as numeracy (Mathematics). Several factors contribute to this shocking situation, such as the absence of the use of meta-cognitive strategies, number strategies, as well as language strategies. The prime goal of this study was to investigate the use of meta-cognitive strategies and Mathematical vocabulary during problem solving by Grade 7 learners. Three primary schools were invited to participate in the qualitative investigation. From these schools three top achievers (one per school) and three under-achievers (one per school) were invited to participate in the quantitative investigation. The study includes the results of the quantitative aspects of the investigation. Learners had to answer questions about predictions, achievements, control, as well as evaluation during the quantitative investigation. During this process, most of the learners predicted that they would do well and evaluated that they did well, but their marks for the questions about their achievements and control were in fact different. It is important to inform Mathematics teachers and learners about meta-cognitive strategies and Mathematical vocabulary, and the influence it can have on the learners’ achievements, as well as the positive effect during the learning of Mathematics. / MEd (Mathematics Education), North-West University, Potchefstroom Campus, 2014